As well as providing the first estimate of the potential bill for the scheme, the National Audit Office(NAO) warned that a shortage of housing and school places could pose a threat to the chances of meeting the pledge.

Costs associated with the initiative fall to different central government departments and councils taking part, and no official total has been given so far.

The sum is uncertain as it depends in large part on the characteristics of those entering the country, the extent to which refugees need medical treatment or welfare services and the extent to which they can gain employment and become self-sufficient, according to the NAO.

Based on department assumptions, it estimated that the cost to the end of 2019/20 could be up to £1.1 billion, and up to £1.73 billion over the lifetime of the project.

The estimated total sum , which includes potential costs for healthcare, education and welfare, equates to £17,340 per refugee per year on average for their first five years in the UK.

Nearly 5,000 houses or flats, and more than 10,000 childcare and school places will be needed for the initiative, according to the NAO.

Its report said: "The future of the programme could be put at risk by local authorities' lack of suitable accommodation and school places."

As of June 2,659 refugees had been resettled in the UK through the programme - 13% of the target, with those arriving dispersed across 118 local authority areas.

Enough "indicative" pledges have been secured from local authorities to meet the aim.

" It is essential that these pledges materialise into firm offers of support as more refugees will need to be resettled each quarter during the remainder of the programme than have been so far", the NAO said.

The report said the scheme expanded the original programme successfully to resettle 1,000 refugees by Christmas.

Amyas Morse, head of the NAO, said: " The programme team achieved a great deal in a short amount of time, resettling much larger numbers of refugees than previous programmes, due in large part to the dedication and goodwill of those involved.

"The characteristics of the refugees arriving in the UK will become clearer over time. With this new information, the programme team must adapt budgets so that no organisation taking part in the programme struggles to participate effectively due to cost pressures."

David Simmonds, of the Local Government Association, said: "We have previously said that we were confident in ensuring that there would be sufficient pledges to support the Government's aim to resettle 20,000 people by 2020 and the Home Office has now confirmed this to be true. The focus must now be on ensuring families are well supported."

A Government spokesman said it is on track to meet the 20,000 commitment.

He added: " We have secured all the local authority pledges required to meet this commitment and the hard work across Government involving the devolved administrations and local authorities will continue until we have turned all of these pledges into places and resettled 20,000 people.

"This is a humanitarian programme and the level of funding enables local authorities to provide vulnerable refugees with a safe environment and the chance to rebuild their lives.

"We ask local authorities to consider carefully whether they have the necessary infrastructure and support networks before a resettlement occurs and we will only resettle individuals to a particular area once we've ensured these arrangements, including school places and housing, are in place."